Application of polynomial chaos expansion in sensitivity analysis of towed cable parameters of the underwater towing system

The key to achieving the optimal design of towed cables, maintaining numerical simulation accuracy, and achieving precise control of the towed body lies in sensitivity analysis. However, the traditional global sensitivity analysis method presents challenges such as high calculation costs and low accuracy. To address these issues, this paper introduces polynomial chaos expansion (PCE) to quantitatively analyse the impact of uncertainties in physical and environmental parameters on the position and attitude of the towed cable. Latin hypercube sampling is employed to obtain sample sets of input parameters, and these samples are applied to the lumped mass method to calculate the end position coordinates of the towed cable, which serves as the output response. PCE is utilized to quantitatively compute the Sobol global sensitivity index of the towed cable parameters. The accuracy of the PCE model is verified, and the optimal degree of basis functions is selected using the bias-variance trade-off. The advantages of PCE are demonstrated by comparing it with the Monte Carlo and Morris methods. The results indicate that PCE accurately calculates the global sensitivity index of towed cable parameters even with a limited sample size. Under the condition of a fixed cable length, the position and attitude of the towed cable are sensitive to the current rate, liquid density, cable diameter, normal drag coefficient, and specific gravity. The feasibility and efficiency of PCE applied to the sensitivity analysis of towed cable parameters is verified, and recommendations for the engineering application of towed cables are summarised.